Question

Below is a table showing the production numbers for a chair factory (where the production numbers are based on chairs being produced per day).

Workers	Total Product (TP)	Average Product (AP)	Marginal Product (MP)	Value of the Marginal Product (VMP)
0	0	-	-	-
1			20
2	60
3		40
4	180
5		46
6	270
7	300
8		40
9			10
10			5

a) Fill in the missing numbers for the TP, AP and MP columns (round to the nearest whole chair)

b) In one sentence explain what the AP of 5 workers being 46 tells us.

c) In one sentence explain what the for MP of the 1^st worker being 20 tells us.

d) Given the fact that each chair produced in our factory can be sold at the market price of $20 per chair, fill in the VMP column (round to the nearest dollar).

e) In one sentence explain what your answer for VMP for the 4^th worker tells us.

f) If the market wage for workers doing manufacturing work (such as chair production) is $300 per day, determine the amount of workers this firm should hire to maximize its profit.

Explain your answer using VMP and the wage.

Answer 1

a ) Ans:

Workers	Total Product ( TP)	Average Product ( AP)	Marginal Product ( MP)
0	0	-	-
1	20	20	20
2	60	30	40
3	120	40	60
4	180	45	60
5	230	46	50
6	270	45	40
7	300	42.85	30
8	320	40	20
9	330	36.66	10
10	335	33.5	5

Explanation:

Average Product = TP / Number of workers

Marginal product = Change in TP / Change in number of  worker

b ) Ans: The AP of 5 workers being 46 tells us that on an average one worker ( from 5 workers ) produces 46 units of output.

c ) Ans: The MP of the 1^st worker being 20 tells us that the total quantity of 20 units of output is produced by 1^st worker.

d ) Ans:  

Workers	Total Product ( TP)	Average Product ( AP)	Marginal Product ( MP)	Value Marginal Product ( VMP ) ( $ )
0	0	-	-	-
1	20	20	20	400
2	60	30	40	800
3	120	40	60	1200
4	180	45	60	1200
5	230	46	50	1000
6	270	45	40	800
7	300	42.85	30	600
8	320	40	20	400
9	330	36.66	10	200
10	335	33.5	5	100

Explanation:

VMP = Price * MP

e ) Ans: The VMP for the 4^th worker is zero. It means the contribution of 4th worker is zero.

f ) Ans: 8 workers

Explanation:

The profit maximization condition is where VMP equals to or greater  than wage rate.

So it is cleared from the above table , at 8 workers the VMP ($400 ) is greater than wage rate ( $300). But at 9 workers the VMP ($200 ) is less  than wage rate ( $300)